Second monitor switches off my iMac during working with Photoshop Tools on this monitor.

I'm afraid I've not seen that issue but it sounds nasty

Resetting Photoshop MAY help - if you get a fix please come back here and let us know

Perhaps try resetting Photoshop preferences?

Resetting restores Photoshop's internal preferences, which are saved when Photoshop closes. If they become corrupt then various issues can occur.

Here’s some info on how to do that:

Restore your preferences using the manual method: https://helpx.adobe.com/photoshop/using/preferences.html#Manually

More:

https://helpx.adobe.com/photoshop/using/preferences.html#reset_preferences

https://helpx.adobe.com/photoshop/using/preferences.html

And

https://community.adobe.com/t5/photoshop-ecosystem-discussions/quick-tips-how-to-reset-photoshop-preferences/td-p/12502668

You may want to backup your settings and your custom presets, brushes & actions before restoring Photoshop's preferences.

Here is general info about that:  https://helpx.adobe.com/photoshop/using/preferences.html#BackupPhotoshoppreferences

Also take a look at the following article and check if that helps: 

https://helpx.adobe.com/photoshop/using/printing-color-management-photoshop1.html

Preferences file location: https://helpx.adobe.com/photoshop/kb/preference-file-names-locations-photoshop.html

On Mac, preference preservation is affected by maxOS permissions, you’ll need to allow Photoshop ‘Full Disk Access’ in your Mac OS Preferences/Security and Privacy

It may even be time to reinstall Photoshop.

It’s recommended that you use the Adobe CC cleaner tool to remove all traces first.

https://helpx.adobe.com/creative-cloud/kb/cc-cleaner-tool-installation-problems.html

Uninstall Photoshop BUT make sure to choose the option “Yes, remove app preference”.

Once that process finishes, start the installation process and look into the “Advanced Options”. Uncheck “Import previous settings and preferences” and choose to “Remove old versions”.

I hope this helps

neil barstow, colourmanagement net :: adobe forum volunteer

google me "neil barstow colourmanagement" for lots of free articles on colour management